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Author Topic: Economics, Ethics, Value Commensurability, General Covariance
Jedi Master
Posts: 92
Post Economics, Ethics, Value Commensurability, General Covariance
on: April 25, 2013, 09:37

"In recent decades, incommensurability has figured prominently in recent philosophical debates over the possibility of moral dilemmas and the plausibility of certain forms of consequentialism in ethics. The incommensurability of various types of moral reason is often seen as explaining how moral dilemmas and other ethical conflicts might be possible. Incommensurability also presents a prima facie challenge to ethical theories that contend that the right thing to do is the action that promotes the most overall good; if value incommensurability is widespread enough to make most values incommensurable with one another, then it seems that the utilitarian calculus is not even theoretically possible."

"General Covariance is all about laws of physics remaining unchanged under an arbitrary but legitimate, transformation of spacetime coordinates."

Intersubjective Utility Comparisons:

However, since one thing can have utility in more than one frame, intersecting content provides a basis for entanglement of utility functions. For example, if there are two hungry people A and B on a desert island and nothing to eat but one mango hanging from a tree, their individual utility functions both acquire the mango as an argument. Indeed, where teamwork has utility - and this is the rule in human affairs - A and B are acquired by each other's utility function (e.g., suppose that the only way A or B can reach the mango is to support or be supported by the other from below).

In a system dominated by competition and cooperation - a system like the real world - this cross-acquisition is a condition of interaction. But given a system with interacting elements, we have a systemic identity, i.e. a distributive self-transformation applying symmetrically to every element (frame) in the system, and this implies the existence of a mutual transformation relating different elements and ultimately rendering them commensurate after all. So "absolute moral relativism" fails in interactive real-world contexts. It's a logical absurdity."

"Why, if there exists a spiritual metalanguage in which to establish the brotherhood of man through the unity of sentience, are men perpetually at each others' throats? Unfortunately, most human brains, which comprise a particular highly-evolved subset of the set of all reality-subsystems, do not fire in strict S-isomorphism much above the object level. Where we define one aspect of "intelligence" as theamount of global structure functionally represented by a given sÎS, brains of low intelligence are generally out of accord with the global syntax D(S). This limits their capacity to form true representations of S (global reality) by syntactic autology [d(S) Éd d(S)] and make rational ethical calculations. In this sense, the vast majority of men are not well-enough equipped, conceptually speaking, to form perfectly rational worldviews and societies; they are deficient in education and intellect, albeit remediably so in most cases. This is why force has ruled in the world of man…why might has always made right, despite its marked tendency to violate the optimization of global utility derived by summing over the sentient agents of S with respect to space and time."

"The above reasoning has important implications. These can be glimpsed by considering that when confronted by paradoxes devolving to a lopsided fixity of the player's subjective frame, we achieved resolutions by letting each frame vary in terms of the other. The analogy with physics is obvious; when a "motionless" observer O1 perceives another O2 to be moving at constant velocity with respect to him, the "moving" observer can turn the tables, regarding himself as motionless and O1 as moving at constant velocity in the opposite direction. This is called "Galilean Relativity". But the story does not end there; relating subjective frames in terms of decision-theoretic invariants like the fixed total value |G| of a game, and the 2x-or-x/2 constraint, invokes analogies with a more complex kind of relativity, the “special relativity” of Einstein. The foregoing treatment suggests that value and expectation are relativistic in the full algebraic sense, not mere "absolutes" that can always be adequately characterized in terms of numeric constants.

Let us expand on this a bit. Economies relate subjective scales of value. People experience need of, and therefore place subjective value on food, shelter, clothing and transportation. Because these goods and services must be gathered, manufactured or performed by specialists, they tend to be concentrated rather than uniformly distributed among the populace. This creates pressure for redistribution, and if redistribution is governed by individual (as opposed to collective) rationality, these items must be exchanged among individuals according to the law of supply and demand. The medium of exchange is called an “economy”. Because individual subjects place different values on different goods and services, values must be defined relative to subjective value scales, and economic transactions translate one subjective value scale into another. The evolution of a consensus regarding the relative values of various goods and services permits the evolution of a convenient universal standard of exchange, “money”, in terms of which this consensus is expressed. Nevertheless, value remains basically subjective in nature, and local deviations from standard valuations thus remain common. Even as an economy freely evolves and economic forces converge, consolidate and split apart, transactions continue to be driven by individual need, and initiated or authorized at the subjective level.

Bearing this in mind, look at a generic economic transaction in the context of a minimal 2-envelope game in which each envelope is held by a competitive player and the 2x-or-x/2 constraint is absent. In almost all cases, the players in the transaction hold different stakes of which the objective values are probably different; one stake will almost certainly be more valuable than the other. “Win” and “loss” may then be defined in the obvious way, the player emerging with the more valuable stake being the “winner” and the other being the “loser”. And the same basic rationale – “if I lose, I lose just what I have, but if I win, I win more than I have” – applies. The only difference is the kind and amount of information available; players in the envelope game have no specific information about the objective values of their stakes, while those involved in normal economic transactions have at least some information from which the relative values of stakes may be subjectively inferred.

Were there really such a thing as absolute intrinsic value, the resolutions given for the Kraitchik and 2-envelopes paradoxes would be final. Each player could reason strategically from an elevated multi-frame perspective to avoid the essential fallacy of these paradoxes. Unfortunately, economic uncertainty makes assessments of absolute value all but impossible; the Kraitchik rationale in effect becomes a subjective vote of confidence in one’s own opinions and projections, and all one can hope to do is allow for the dynamics of interacting subjective frames. Although the Kraitchik and 2-envelopes paradoxes deal with games whose rules seem artificial, these rules turn out to be general; interframe differentials in subjective value account for the ubiquity and validity of the Kraitchik rationale in games which locally appear to be 0-sum, but need not be so in the wider contexts to which the players are subjectively linking them…contexts that ultimately merge in the global economy, precipitating cooperation and competition leading to expectative conflicts. Indeed, relativism based on subjective value differentials expressed in a global “spacetime” of transactions or "economic events" is what allows a locally 0-sum game to be globally advantageous, contributing to an overall win-win scenario in which the economy undergoes real expansion.

Once we suspend the 0-sum criterion that makes the Kraitchik rationale “fallacious”, its status changes from that of a fallacy to that of a true “law of economics”. Being the distributed basis of collective demand-pull and cost-push inflationary scenarios – the former works in specialized subeconomies whose players compete for resources to produce a certain kind of salable item, while the latter pushes the resulting inflation outward across the subeconomic boundary - this law drives inflation; but since the creation of wealth is driven by subjective motivation, it is also what drives legitimate economic expansion. Two real-world conditions, ambiguity of value and value differentials between subjective frames, create relativistic scenarios whose expansive and inflationary effects diffuse throughout the economy via inflationary mechanisms whose subjective basis was previously not well-understood. In self-interestedly betting on themselves and the futures of their local subeconomies, players create the global economy and determine the global parameters of value. Here, the Kraitchik and 2-envelopes paradoxes give way to an economic analogue of paradoxes involving sets that both determine and are determined by their elements, e.g. the paradoxes of Cantor and Russell.

What, then, are the rules in terms of which frame-invariant economic calculations should be made, and these abstract economic paradoxes resolved in the real-world economy? Unfortunately, the answer – a general theory of economic relativity - will have to be the subject of a future paper."

Jedi Master
Posts: 92
Post Re: Economics, Ethics, Value Commensurability, General Covariance
on: May 2, 2013, 16:47

"Beyond the evolution of physical laws, Smolin goes to some lengths to show how much can change if we take time as fundamental. From the weirdness of quantum mechanics to the mystery of space and its three dimensions, Smolin argues that many of the stubborn problems in modern foundational physics can be overcome once time is restored to its rightful place as the foundation of reality."

"In physics, the term general covariance is meant to indicate the property of a physical system or model (in theoretical physics) whose configurations, action functional and equations of motion are all equivariant under the action of the diffeomorphism group on the smooth manifold underlying the spacetime or the worldvolume of the system. The archetypical example of a generally covariant system is of course Einstein-gravity / “general relativity”.

I indicate here how general covariance has a natural formalization in homotopy type theory, hence internal to any ∞-topos. For background and all details see at general covariance on the nLab, and the links given there."

"The Reign of Relativity »
General Covariance and the “Relativized A Priori”

Two Roads from Kant
(p. 13 ) General Covariance and the “Relativized A Priori”
The Reign of Relativity
Thomas Ryckman
Oxford University Press
A tension within Kant’s Transcendental Analytic, regarding the combination of the “active” faculty of understanding with the “passive” faculty of sensibility, underlies the distinct appraisals in 1920 by Hans Reichenbach and Ernst Cassirer of constitutive but “relativized” a priori principles in the GTR. Reichenbach’s “principles of coordination” presuppose Schlick’s conception of cognition as a coordination of formal concepts to objects of perceptual experience, and are shown to be consonant only with the commitments of scientific realism. Cassirer’s rejection of the “active”/“passive” dichotomy promoted his conception of general covariance as a high level principle of objectivity, much in accord with Einstein’s own later views, as recently articulated in the literature on the “Hole Argument.” In particular, the principle of general covariance is shown to place significant constraints on field theories, a point noted by David Hilbert and implicit in the work of Emmy Noether."

"Whereas Einstein took general covariance to characterize GTR, Kretschmann thought it merely a formal feature that any theory could have. Anderson and Friedman analyzed substantive general covariance as the lack of absolute objects, fields the same in all models. Some extant counterexamples and a new one involving the electron spinor field are resolved. However, Geroch and Giulini diagnose an absolute object in GTR itself in the metric's volume element. One might instead analyze substantive general covariance as formal general covariance achieved without hiding preferred coordinates as scalar "clock fields," recalling Einstein's early views. Theories with no metric or multiple metrics make the age of the universe meaningless or ambiguous, respectively, so the ancient and medieval debate over the eternity of the world should be recast."

Jedi Master
Posts: 92
Post Re: Economics, Ethics, Value Commensurability, General Covariance
on: June 14, 2013, 14:21

"Although Arrow's theorem is a mathematical result, it is often expressed in a non-mathematical way with a statement such as "No voting method is fair," "Every ranked voting method is flawed," or "The only voting method that isn't flawed is a dictatorship". These statements are simplifications of Arrow's result which are not universally considered to be true. What Arrow's theorem does state is that a deterministic preferential voting mechanism - that is, one where a preference order is the only information in a vote, and any possible set of votes gives a unique result - cannot comply with all of the conditions given above simultaneously.

Arrow did use the term "fair" to refer to his criteria. Indeed, Pareto efficiency, as well as the demand for non-imposition, seems acceptable to most people.

Various theorists have suggested weakening the IIA criterion as a way out of the paradox. Proponents of ranked voting methods contend that the IIA is an unreasonably strong criterion. It is the one breached in most useful voting systems. Advocates of this position point out that failure of the standard IIA criterion is trivially implied by the possibility of cyclic preferences. If voters cast ballots as follows:

1 vote for A > B > C
1 vote for B > C > A
1 vote for C > A > B

then the pairwise majority preference of the group is that A wins over B, B wins over C, and C wins over A: these yield rock-paper-scissors preferences for any pairwise comparison. In this circumstance, any aggregation rule that satisfies the very basic majoritarian requirement that a candidate who receives a majority of votes must win the election, will fail the IIA criterion, if social preference is required to be transitive (or acyclic). To see this, suppose that such a rule satisfies IIA. Since majority preferences are respected, the society prefers A to B (two votes for A>B and one for B>A), B to C, and C to A. Thus a cycle is generated, which contradicts the assumption that social preference is transitive.

So, what Arrow's theorem really shows is that any majority-wins voting system is a non-trivial game, and that game theory should be used to predict the outcome of most voting mechanisms.[9] This could be seen as a discouraging result, because a game need not have efficient equilibria, e.g., a ballot could result in an alternative nobody really wanted in the first place, yet everybody voted for.

Remark: Scalar rankings from a vector of attributes and the IIA property. The IIA property might not be satisfied in human decision-making of realistic complexity because the scalar preference ranking is effectively derived from the weighting—not usually explicit—of a vector of attributes (one book dealing with the Arrow theorem invites the reader to consider the related problem of creating a scalar measure for the track and field decathlon event—e.g. how does one make scoring 600 points in the discus event "commensurable" with scoring 600 points in the 1500 m race) and this scalar ranking can depend sensitively on the weighting of different attributes, with the tacit weighting itself affected by the context and contrast created by apparently "irrelevant" choices. Edward MacNeal discusses this sensitivity problem with respect to the ranking of "most livable city" in the chapter "Surveys" of his book MathSemantics: making numbers talk sense (1994)."'s_impossibility_theorem

"The voting paradox (also known as Condorcet's paradox or the paradox of voting) is a situation noted by the Marquis de Condorcet in the late 18th century, in which collective preferences can be cyclic (i.e. not transitive), even if the preferences of individual voters are not. This is paradoxical, because it means that majority wishes can be in conflict with each other. When this occurs, it is because the conflicting majorities are each made up of different groups of individuals."

"The Borda count is a single-winner election method in which voters rank candidates in order of preference. The Borda count determines the winner of an election by giving each candidate a certain number of points corresponding to the position in which he or she is ranked by each voter. Once all votes have been counted the candidate with the most points is the winner. Because it sometimes elects broadly acceptable candidates, rather than those preferred by the majority, the Borda count is often described as a consensus-based electoral system, rather than a majoritarian one."

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